Juan, Tanks for your answer and sorry for the confusion that was just a chronological order. First step was nls which returned the error message Second step: defined the scalars (which I wrote before the the nls code Third step: Re estimated nls, with arbitrarily defined scalars i.e. scalars = ... (...) nls...end nls However, as discussed in the 2008 thread, I wanted to 'constrain' the coefficients to be non-negative, but nls returned a negative estimate on w5. An alternative is to set up a quadratic programming excel solver model. I wanted to use nls, to a) verify my excel results an b) to retrive some standrad errors, for t-Tests. Kind regards, Jan Von meinem iPad gesendet Am 29.04.2014 um 18:38 schrieb "Juan C. Estévez" <ecadrian.estevez@usc.es<mailto:ecadrian.estevez@usc.es>>: Dear All, I was trying to estimate a non-linear least squares regression and found the following discussion from April 2008. http://lists.wfu.edu/pipermail/gretl-users/2008-April/002337.html I changed the code, so that it would accommodate my “model”. All Xi’s as well as Y are time series. Unfortunately, when I estimate the model, I get an error: b1: expect scalar or vector. ... But don´t you get this error because you define the scalars after de 'nls ... end nls' command, instead of defining them before? nls Y= w1*X1+ w2*X2 + w3*X3 + w4*X4 + w5*X5 + w6*X6 w1=b1^2 w2=b2^2 w3=b3^2 w4=b4^2 w5=b5^2 w6=1-w1-w2-w3-w4-w5 params b1 b2 b3 b4 b5 end nls After this, I tried to define arbitrary scalars as starting values (no theory, just numbers that came to my mind) scalar b1=0.1 scalar b2=0.2 scalar b3=-0.05 scalar b4=0.03 scalar b5=-0.015 _______________________________________________ Gretl-users mailing list Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu> http://lists.wfu.edu/mailman/listinfo/gretl-users

Jack, Thank you for your answer. You are correct, that is exactly what I am trying to do. Actually, I thought, that the prior post was just about the same topic. I will try to implement your suggestions tomorrow, as I have no access to gretl at the moment. Again, many thanks and please forgive my ignorance in these kind of (basic?) econometrics. Jan

Sven, thank you for clarification. Afterwards, I tried to adapt Jack's code to my problem (I have six independent variables x1...x6, therefore I think I need b1...b5 parameters, with exponential transformations e1...e5 and expand the den to den=1+e1+...+e5 to finally get w1...w5). This, however lead me to another problem. The calculation of the jacobian failed. I guess this is due to multicollienarity issues (correlations are high - between 0.83 and 0.97) and because it works, when I omit x6 and adapt the model accordingly. I also tried standard OLS-Coefficients as starting values for the b's but it did not change (which might be no surprise). However, using the wi=bi^2 parameterization, gretl has no problem with calculating the jacobian and runs through the estimation procedure (that came as surprise), but as you said there is the possibility that the last coefficient is negative. Once I again, I also want to thank Jack for providing the code. All the best, Jan -----Ursprüngliche Nachricht----- Von: Plus.line MailSystem [mailto:cyrus@mailer.plusline.de] Im Auftrag von Sven Schreiber Gesendet: Mittwoch, 30. April 2014 09:03 An: gretl-users(a)lists.wfu.edu Betreff: Re: [Gretl-users] Non-linear least squares Am 29.04.2014 20:17, schrieb Jan Tille: Jan, I looked at the old messages from 2008, and your question is perfectly ok. In fact, I think back then Jack gave a partly incorrect answer (unbelievable as it may sound), because in his example only the first two coefficients were actually restricted to be non-negative, not the last one. Hence results such as yours can happen. Jack's new answer is the one to follow (unless we find a mistake in another six years time...). cheers, sven _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users

Jack, Thank you for your hint. By "shares", do you mean the "SSR" values? Indeed, in your example, they are around 50 and using my data SSR starts at around 0,01 and converges towards 0,00632... and stops after 49 iterations. This is when gretl tells me that the jacobian cannot be calculated. If you mean the w's, my estimated w5 (if I only use x1...x5) is zero (0,0000000039...). Except for choosing other data/independent variables. Is there any way to work around that? Another question that I was asking myself, concerns the t-values (or standard errros). As they are calculated for the b's, they likely have to be transformed to represent t-values for the estimated w's. I guess this has to be done in another way, then just using exp() and divide it by exp(bi)/(1+sum(exp(...)). One possibility that I can imagine is to use the w's from the nls estimation and, calculate the "residuals" for the linear model (which is bluntly the way how it would be done via standard OLS). But I could also imagine that this might lead to grossly misleading standard error estimates. All the best, Jan -----Ursprüngliche Nachricht----- Von: Plus.line MailSystem [mailto:cyrus@mailer.plusline.de] Im Auftrag von Riccardo (Jack) Lucchetti Gesendet: Mittwoch, 30. April 2014 12:16 An: Gretl list Betreff: Re: [Gretl-users] Non-linear least squares On Wed, 30 Apr 2014, Jan Tille wrote: That's correct. That's also likely to happen when one or more of your "shares" are near 0. See what happens with analytical gradients, as in <hansl> nls y = w1 * x1 + w2 * x2 + (1-w1-w2) * x3 e1 = exp(b1) e2 = exp(b2) den = 1 + e1 + e2 w1 = e1 / den w2 = e2 / den deriv b1 = w1 * (1-w1) * x1 deriv b2 = w2 * (1-w2) * x2 end nls --verbose </hansl> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------

On Wed, 30 Apr 2014, Riccardo (Jack) Lucchetti wrote: I wrote a few functions to compute a regression in which coefficients are constrained to be strictly positive and sum to one. This was quite fun, but not vey much tested. It would be VERY nice if someone did some more work on this and turned it into a function package (hint, hint!) <hansl> set echo off set messages off function matrix shares(matrix b) matrix e = exp(b | 0) scalar den = sumc(e) return e ./ den end function function matrix dshares(matrix b) matrix p = shares(b) scalar k = rows(b) matrix ret = -p .* p[1:k]' ret[diag] += p[1:k] return ret end function function bundle OLS_shares(series y, list X) scalar k = nelem(X) # initalisation ols y X --quiet matrix b = ($coeff .> 0.01) ? $coeff : 0.01 matrix b = ln(b[1:k-1]) - ln(b[k]) nls y = lincomb(X, p) p = shares(b) J = dshares(b) deriv b = {X} * J end nls --quiet bundle mdl mdl["Xnames"] = varname(X) mdl["coeff"] = p mdl["vcv"] = qform(J, $vcv) return mdl end function function void printout(bundle model) string parnames = model.Xnames matrix cs = model.coeff ~ sqrt(diag(model.vcv)) modprint cs parnames end function # ---------------------------------------------------- nulldata 1000 x1 = normal() x2 = normal() x3 = normal() y = 0.3*x1 + 0.01*x2 + 0.69*x3 + normal() list X = x1 x2 x3 b = OLS_shares(y, X) printout(b) </hansl> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------